S(t)=150-4.9t^2

Solution for S(t)=150-4.9t^2 equation:

(S)=150-4.9S^2

We move all terms to the left:

(S)-(150-4.9S^2)=0

We get rid of parentheses

4.9S^2+S-150=0

a = 4.9; b = 1; c = -150;
Δ = b2-4ac
Δ = 12-4·4.9·(-150)
Δ = 2941
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{2941}}{2*4.9}=\frac{-1-\sqrt{2941}}{9.8}
$
$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2941}}{2*4.9}=\frac{-1+\sqrt{2941}}{9.8}
$